

A036234


Number of primes <= n, if 1 is counted as a prime.


20



1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20
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OFFSET

1,2


COMMENTS

This sequence is the largest nondecreasing sequence a(n) such that a(Prime(n)1) = n.  Tanya Khovanova, Jun 20 2007
Partial sums of A080339.  Jaroslav Krizek, Mar 23 2009
Let G(n) be the graph whose vertices represent integers 1 through n, and where vertices a and b are adjacent iff gcd(a,b)>1. Then a(n) is the independence number of G(n).  Aaron Dunigan AtLee, May 23 2009
a(1)=1; a(n)= max[A061395(n), A061395(n1)].  Jacques ALARDET, Dec 28 2011
It appears that a(n) is the minimal index i for which binomial(k*prime(i), prime(i)) mod prime(i) = k. For example, binomial(11*prime(n), prime(n)) mod prime(n) produces the sequence 1,2,1,4,0,11,11,11,11 and a(11)=6. It also appears that binomial(k*prime(a(n)1), prime(a(n)1)) mod prime(a(n)1) = 0 iff k is prime.  Gary Detlefs, Aug 05 2013
a(n) is the number of noncomposite numbers <= n. The noncomposite number are in A008578.  Omar E. Pol, Aug 31 2013
Number of distinct terms in nth row of the triangle in A080786.  Reinhard Zumkeller, Sep 10 2013


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A000720(n) + 1.  Jaroslav Krizek, Mar 23 2009


MAPLE

A036234 := proc(n)
if n = 1 then
1;
else
1+numtheory[pi](n) ;
end if;
end proc: # R. J. Mathar, Jan 28 2014


MATHEMATICA

Table[PrimePi[n] + 1, {n, 100}] (* Tanya Khovanova, Jun 20 2007 *)


PROG

(Haskell)
a036234 = (+ 1) . a000720  Reinhard Zumkeller, Sep 10 2013
(PARI) a(n)=primepi(n)+1 \\ Charles R Greathouse IV, Apr 29 2015


CROSSREFS

Cf. A000720, A080339, A147693.
Sequence in context: A038567 A185195 A192512 * A061091 A196241 A086592
Adjacent sequences: A036231 A036232 A036233 * A036235 A036236 A036237


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



